#### Vol. 304, No. 2, 2020

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Regularity of quotients of Drinfeld modular schemes

### Satoshi Kondo and Seidai Yasuda

Vol. 304 (2020), No. 2, 481–503
##### Abstract

Let $A$ be the coordinate ring of a projective smooth curve over a finite field minus a closed point. For a nontrivial ideal $I\subset A$, Drinfeld defined the notion of structure of level $I$ on a Drinfeld module.

We extend this to that of level $N$, where $N$ is a finitely generated torsion $A$-module. The case where $N={\left({I}^{-1}∕A\right)}^{d}$, where $d$ is the rank of the Drinfeld module, coincides with the structure of level $I$. The moduli functor is representable by a regular affine scheme.

The automorphism group ${Aut}_{A}\left(N\right)$ acts on the moduli space. Our theorem gives a class of subgroups for which the quotient of the moduli scheme is regular. Examples include generalizations of ${\Gamma }_{0}$ and of ${\Gamma }_{1}$. We also show that parabolic subgroups appearing in the definition of Hecke correspondences are such subgroups.

##### Keywords
Drinfeld modular schemes, Drinfeld level structures, regularity
Primary: 11F32
Secondary: 14G35